Theta Function
In mathematics, theta functions are special functions of several complex variables. They are important in many areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms. They have also been applied to soliton theory. When generalized to a Grassmann algebra, they also appear in quantum field theory.
The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function. In the abstract theory this comes from a line bundle condition of descent.
Read more about Theta Function: Jacobi Theta Function, Auxiliary Functions, Jacobi Identities, Theta Functions in Terms of The Nome, Product Representations, Integral Representations, Explicit Values, Zeros of The Jacobi Theta Functions, Relation To The Riemann Zeta Function, Relation To The Weierstrass Elliptic Function, Some Relations To Modular Forms, A Solution To Heat Equation, Relation To The Heisenberg Group, Generalizations
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